DEPENDENCE OF SIGNAL POWER ON PARAMETERS 



201 



target, and scau-to-scan integration. If the scanning 

 rate is suflBciently rapid (faster than 10 rpm) the 

 signal visibility will be independent of the antenna 

 rotation rate. Faster rotation rates intercept a smaller 

 number of pulses for each revolution, but there are a 

 greater number of scan-to-scan integrations which just 

 make up for the deficit. However, below the critical 

 speed of about 10 rpm, scan-to-scan integration will 

 not take place, and the signal threshold power will be 

 proportional to the square root of the antenna rotation 

 rate. This improvement in signal visibility at slower 

 scan rates will continue until the antenna is on the 

 target, during each revolution for approximately 6 

 sec, whereupon the visibility is essentially that of a 

 "searchlighting" set. Thus the total scanning loss is 

 given by the rather simple formula 



Loss = - , 



where Ft is the fraction of time that the system is on 

 target during the scanning procedure. Ordinarily this 

 scanning loss amounts to approximately 10 db in an 

 average radar system, requiring a signal perhaps 10 

 times as large as the necessary amount for detection 

 wliile searchlighting. It is important that this formula 

 be used only where scan-to-scan integration takes 

 place. 



Discussion 



While this paper has specifically been limited to 

 noise considerations, it seemed reasonable to hope that 

 the same general considerations could be applied in 

 determining the visibility of signals in various types 

 of clutter, in particular the simpler types which are 

 echoes from rain and snow. If the mechanisms involved 

 were more thoroughly understood, the fundamentals 

 of the problem would be understood too and could be 

 put together in a coherent form. 



The shape of the response curve has been considered 

 by the author and is known to have some effect, but 

 the experimental approach to various shape factors 

 has been rather limited. In the work presented here 

 the response curve of the receivers involved has been 

 that of a so-called double-tuned circuit, whose ampli- 

 tude response is proportional to 



[-©T* 



where w is the frequency difference between the fre- 

 quency under measurement and the center of the band. 



(Do is the V2 bandwidtli. The difEerence between this 

 response curve's performance and that of a multiply 

 narrowed, synchronously tuned, intermediate ampli- 

 fier, which has Gaussian response, was not observable 

 experimentally. Theoretically also, there is little dif- 

 ference. It is felt that the considerations may not apply 

 in extreme cases of sharp-edged amplifiers or in single 

 single-tuned circuits but that in other cases the same 

 answers do apply. 



The question was raised as to the dependence of 

 signal threshold on pulse recurrence rate. In all the 

 other parameters the visibility of the signal is pro- 

 portional to the signal energy. The author found that 

 for a given average power the visibility is distinctly 

 better if you concentrate more energy into each pulse 

 and separate the pulses by longer intervals. In other 

 words, the threshold is proportional to the energy per 

 pulse but inversely proportional to the square root 

 of the repetition frequency. This settles a disagree- 

 ment between two groups, one of which believes visi- 

 bility would be found independent of pulse repetition 

 rate and the other that it depends on average energy. 

 The answer lies between the two views. In this matter 

 of visibility it is interesting to recall that the first suc- 

 cessful radar, which was giving ranges up to 25 miles 

 in 1936, had a receiver bandwidth of about 200 kc and 

 a pulse length of 5 /isec, a combination which lies on 

 the peak of the maximum visibility curve. The pulse 

 length on the radar screen was about 3 mm. The curve 

 for optimum visibility peaks at 1 mm and does not 

 decline very rapidly for longer pulses, so that, too, was 

 near the optimum value. The first production radar for 

 use in the fleet had a pulse length of about 3 /xsec and 

 a bandwidth of about 300 kc, which is again on the 

 jjeak of the visibility curve, and its visible pulse was 

 about 2 mm long on the screen. This was of course not 

 entirely accidental but was fortunate, nevertheless. 

 The preproduction model of this radar was built in 

 1938. 



The author discussed the effect of fluctuating sig- 

 nals in scanning as distinct from the steady signals 

 which had been employed in the experiments described. 

 In the case of signal fluctuation, it is necessary first to 

 define the signal amplitude in such a way that analy- 

 sis is applicable. Employing the average value as a 

 criterion, the visibility of fluctuating signals may ac- 

 tually prove greater than for steady signals. If the 

 peak value of a fluctuating signal is taken as the signal 

 threshold power, the visibility is probably poorer than 

 for a steady echo, but it is felt that the result would 



